Speaking in front of a photograph of Benito Mussolini at CasaPound's Rome headquarters, Simone di Stefano does not hesitate when asked if he subscribes to the Italian dictator's brand of fascism.

"It's our point of reference, a vision of the state and the economy and the concept of sacrifice," said Di Stefano, who is vice president of CasaPound, the movement that reportedly has 5,000 members in Italy, alongside 15 loyal local councillors and the support of key officials at Rome city hall, where the mayor, Gianni Alemanno, is himself a former neo-fascist.

Last year, a concert in Rome by the rock band led by CasaPound's president, Gianluca Iannone, was sponsored by one of the capital's borough councils. By holding cultural debates on themes as diverse as Che Guevara and Jack Kerouac, CasaPound has sought to separate itself from Italy's old-style, street-fighting neo-fascists. The group is named after Ezra Pound, the American poet who sided with Mussolini during the war.

Mussolini's racial laws were "a mistake," says Di Stefano. "We believe in the national community and the Jews in Italy are part of that." And as for Pound's own antisemitism, "at the time it was very common throughout the world".

The organisation steers clear of what Di Stefano calls fascist "nostalgia" – fascist salutes are saved for funerals – and focuses on promoting cheap housing and occupying empty properties. Eighteen families live in CasaPound's Rome base, a disused state property it has occupied since 2003. "The city hall wouldn't evict us now, we are a cultural point of reference," said 35-year-old Di Stefano.

The movement also runs a phone helpline for Romans falling victim to loan sharks, and dispatches members to help out during natural disasters, like the Abruzzo earthquake in 2009 and this autumn's floods in Liguria.

CasaPound's approach to economics is pure Mussolini "We would like to see communications, transport, energy and health renationalised and the state constructing houses which it then sells at cost to families," said Di Stefano. On immigration, the stance is typical of the far right. "We want to stop it," says Di Stefano. "Low-cost immigrant workers mean Italians are unable to negotiate wages, while the immigrants are exploited."

Left-wing associations have frequently accused supporters of CasaPound of violently attacking their members at demonstrations, and have claimed the group acts as a cover for young men looking for trouble.

"In Rome, fascists assault people but are protected and unpunished," Pierluigi Bersani, head of the opposition Democratic Party told a rally on Saturday.

Di Stefano denied the allegation, saying CasaPound was itself the victim of attacks by leftists, citing an assault on its headquarters in Cuneo in northern Italy.

He also defended the behaviour of CasaPound supporters – who have got into the habit of whipping each other with their belts in the moshpit during gigs by Iannone's band

"It's a bit like Fight Club, a way to risk pain, to confront yourself in way society does not allow," he said. "We also go on mountain walks, it's a similar concept."